Results 41 to 50 of about 47,626 (83)
Quantum groups, Yang-Baxter maps and quasi-determinants
, 2017 For any quasi-triangular Hopf algebra, there exists the universal R-matrix, which satisfies the Yang-Baxter equation. It is known that the adjoint action of the universal R-matrix on the elements of the tensor square of the algebra constitutes a quantum ...
Tsuboi, Zengo
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On deformation theory of quantum vertex algebras [PDF]
, 2005 We study an algebraic deformation problem which captures the data of the general deformation problem for a quantum vertex algebra. We derive a system of coupled equations which is the counterpart of the Maurer-Cartan equation on the usual Hochschild ...
Grosse, Harald, Schlesinger, Karl-Georg
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Twisted Configurations over Quantum Euclidean Spheres
, 2002 We show that the relations which define the algebras of the quantum Euclidean planes $\b{R}^N_q$ can be expressed in terms of projections provided that the unique central element, the radial distance from the origin, is fixed.
Connes +9 more
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Fusion in the entwined category of Yetter--Drinfeld modules of a rank-1 Nichols algebra
, 2012 We rederive a popular nonsemisimple fusion algebra in the braided context, from a Nichols algebra. Together with the decomposition that we find for the product of simple Yetter-Drinfeld modules, this strongly suggests that the relevant Nichols algebra ...
A. Bruguières +56 more
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Topological Hopf algebras, quantum groups and deformation quantization
, 2003 After a presentation of the context and a brief reminder of deformation quantization, we indicate how the introduction of natural topological vector space topologies on Hopf algebras associated with Poisson Lie groups, Lie bialgebras and their doubles ...
Bonneau, Philippe, Sternheimer, Daniel
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Local derivations of quantum plane algebra
Communications in Algebra, 2023– Let k be a field and q∈k* not a root of unity. We prove that on the quantum plane algebra Pq(k)=kq[x,y] any local derivation is a derivation.
A. Louly
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The t-analogs of q-characters at roots of unity for quantum affine algebras and beyond
, 2003The q -characters were introduced by Frenkel and Reshetikhin [The q -characters of representations of quantum affine algebras and deformations of W -algebras, in: Recent Developments in Quantum Affine Algebras and Related Topics, in: Contemp. Math., vol.
D. Hernandez
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Quantization of the derivation Lie algebra over quantum torus
Communications in Algebra, 2023Recently, Lie bialgebra structures of the derivation Lie algebra over quantum torus were determined. In this paper, we use the general method of quantization by a Drinfel’d twist to quantize these algebras with their Lie bialgebra structures and present ...
Shuoyang Xu, Xiaoqing Yue
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BV Structure on Hochschild Cohomology of Quantum Exterior Algebra with Two Variables
Algebra Colloquium, 2023Let [Formula: see text] over a field [Formula: see text]. We give a clear characterization of the Batalin-Vilkovisky algebraic structure on Hochschild cohomology of [Formula: see text] for any [Formula: see text], and the Gerstenhaber algebraic structure
B. Hou, Jinzhong Wu
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